Question

The traffic lights at three different road crossings change after every 48 seconds, 72
seconds and 108 seconds respectively. If they change simultaneously at
7 sm. at what time will they change simultaneously again?​

Answer 1

Answer:

7:07:12 a.m

Step-by-step explanation:

The traffic light at three different road crossing change after every 48 seconds,72 seconds and 108 seconds respectively.

So let us take the LCM of the given time that is 48 seconds, 72 seconds, 108 seconds

⇒ 48 = 2 × 2 × 2 × 2 × 3

⇒ 72 = 2 × 2 × 2 × 3 × 3

⇒ 108 = 2 × 2 × 3 × 3 × 3

Hence LCM of 48, 72 and 108 = (2 × 2 × 2 × 2 × 3 × 3 × 3)

LCM of 48, 72 and 108 = 432

So after 432 seconds they will change simultaneously

We know that

60 seconds = 1 minute

so on dividing 432 / 60 we get 7 as quotient and 12 as reminder

Hence, 432 seconds = 7 min 12 seconds

∴ The time = 7 a.m. + 7 minutes 12 seconds

Hence the lights change simultaneously at 7:07:12 a.m

Answer 2

Step-by-step explanation:

The traffic light at three different road crossing change after every 48seconds,72seconds and 108seconds respectively

So,

48=2×2×2×2×3

72=2×2×2×3×3

108=2×2×3×3×3

Therefore, L.CM of 48,72,108 is

(2×2×2×2×3×3×3)

=432

So, time when they change again =432seconds

But we need to find time after 7am So, first we convert 432seconds into minutes.

Time=432second

=

60

432

minutes

∴Time=7 minutes12 seconds

Thus,

Required time =7am+7minutes 12seconds

=7:07:12am

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